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Theorem 19.8wOLD 1693
 Description: Obsolete version of 19.8w 1660 as of 4-Dec-2017. (Contributed by NM, 1-Aug-2017.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
19.8wOLD.1 (φxφ)
Assertion
Ref Expression
19.8wOLD (φxφ)

Proof of Theorem 19.8wOLD
StepHypRef Expression
1 19.8wOLD.1 . . . . 5 (φxφ)
2 notnot 282 . . . . 5 (φ ↔ ¬ ¬ φ)
32albii 1566 . . . . 5 (xφx ¬ ¬ φ)
41, 2, 33imtr3i 256 . . . 4 (¬ ¬ φx ¬ ¬ φ)
54spnfw 1670 . . 3 (x ¬ φ → ¬ φ)
65con2i 112 . 2 (φ → ¬ x ¬ φ)
7 df-ex 1542 . 2 (xφ ↔ ¬ x ¬ φ)
86, 7sylibr 203 1 (φxφ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  ∃wex 1541 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-9 1654 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by: (None)
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